I means when we select installing Linux from the CD/USB onto a hard disk.

I was feeling more "comfortable" by ensuring the system has internet access during installation. However I am unsure if that is necessary. I think the answer is "no, not necessary" but is there anyone who can confirm?

it depends on the CD/USB, there are two kind of installs available: one does not need net during install, the second will need that (usually that is named net install)

It also depends on the distro. Some are requiring net access during the installation. Which one are you trying?

My download and installation is based on the iso of Linus Mint 18 Sarah (32 bit Mate desktop) given by the following link:
https://www.linuxmint.com/download.php

Linux Mint 18 does not need networking. If you are doing an offline installation, you will have to do extra work to install any special applications that are not on the installation DVD.

If you have internet access, Mint will download the media codecs during installation. If you haven't, it will give you the chance to do it from the first welcome screen. If you don't do it then, you can find an installer in the menu under sound and video.

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If you do allow Mint access to the Internet it will generally sort out any connection dialogue (Router access and password) by asking you for the details required. You also have the added bonus of, after installation, it'll flag up the update manager to allow you to update any revised packages from the versions supplied on the CD/DVD to the current version.

Play Bonny!

But it is recommended to have a connection.
But it is not entirely necessary unless some advanced options were chosen.

Nice to see this being an interesting subject. Thanks all for your contribution.

My mum's XP (that's why I like to try out Linux) computer normally has a wireless connection to home wireless router. When installing Mint I purposely ran a very long cat 5 cable to "ensure" it is connected. I wonder if that's necessary?

In other words I wonder if Linux Mint would have prompted me to enter wifi details. How about the case with most other Linux distros (other Linux favours are interesting, may try on other old laptops later. like Ubuntu or Redhat)?

That's the path I'd choose, to at least get the system updated/upgraded/patched and then try wireless.

See also How to install software on Linux Mint and
https://sites.google.com/site/easylinuxtipsproject/Home

Ordinarily, internet access is used if available, e.g. to look for and to apply the most-recent available set of patches.

I did the same as you; installed Mint 17.3 on my Asus Netbook then disconnected it and clicked on the network connection icon in the panel, RHS. Enabled the WiFi, selected my router and logged in with the password. I think it would prompt you for WiFi setup if you hadn't already connected the cable.
I prefer my desktop stuff to be cabled as I reckon it's more secure and also faster.

Play Bonny!

I have several Debian machines, enough so that I keep a local debian mirror for the i386, amd64 architectures and source packages. But if you don't have a local mirror you probably want an Internet connection. Linux loses a lot without Internet.